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Country Boy

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  1. If I understand what you have written, $3975,3- F_{35}cos(26,6)+ F_{32}cos(26,6)= 0$ so, adding $F_{35}cos(26,6)- 3975,3$ to both sides, $F_{32}cos(26,6)= F_{35}cos(26,6)- 3975,3$ and then, dividing both sides by cos(26,6), $F_{32}= F_{35}- \frac{3975,3}{cos(26,6)}$.You are told that $F_{35}= 50326,9$ and can use a calculator to determine that cos(26,6)= 0.894. Put those numbers in and do the arithmetic!
  2. I would write every vector in terms of components. T= <-22900, 0>, Weng= <0, -24525>. The sum of those two forces is <-22900, -24525> and the two forces, "45" and "35" must offset that. Taking the force in vector "45" to be "x" and in vector "35" to be "y" we have "45"= <0, x> and "35"= <0.6y/1.34, 1.2y/1.34>= <0.45y, 0.90y>. The sum of those is <0.45y, x+ 0.90y> and that must equal <22900, 24525> so we have 0.45y= 22900 and x+ 0.90y= 24525. From the first y= 22900/0.45= 50,889. Then the second is x+ 45800= 24525 so x= 24525- 45800= -21275. So vector "45" is <0, -21275> and "35" is <50899(.45), 50899(.90)>= <22904.55, 45809.1>. The others are done the same way.
  3. Any linear function of x can be written f(x)= ax+ b for numbers a and b. You are told that f(2002)= 120= 2002a+ b and f(2013)= 212= 2013a+ b. Solve the equations 2002a+ b= 120 and 2013a+ b= 212 for a and b.
  4. No, because such a "set of points" would not be connected so not a line in the geometric sense.
  5. When I click on that link I get a message that says "you do not have permission to do that"!
  6. Well, you can't define or calculate the derivative of a function using only the four arithmetic operations. I would have thought you would have learned that in whatever course you were introduced to the derivative. You have to have the concept of a "limit" as well: [tex]\frac{df}{dx}(a)= \lim_{h\to 0} \frac{f(a+ h)- f(a)}{h}[/tex].
  7. If I am understanding this correctly, a fraction represents a terminating decimal (so there is an "end") if and only if the denominator has factors of "2" and "5" only. How many decimal places is a little harder. 1/2= .5, 1/4= 1/2^2= .25, 1/8= 1/2^3= .125, 1/10= 1/(2*5)= 0.1, 1/16= 1/2^4= .0625, 1/20= 1/(2^2*5)= .05, etc. Do you see a pattern?
  8. Okay, your teacher clearly expects you to know what the "LCM" method is! Do you? (My first thought was "Least Common Multiple" but that might not apply here.)
  9. I don't understand the purpose of this thread. Have you ever actually taken a class in algebra?
  10. Did you listen carefully to this? The first person clearly say "light appears to slow down" while the other two are referring to the average speed of light through the substance. They are all saying the same thing everyone here is saying: Light moves from one atom to another at speed c but takes some time interacting with each atom or molecule so that the average speed through the substance is lower than c.
  11. Which statistical test to use will depend strongly on what the data is.
  12. Pretty much by definition of "number line" every point on a number line corresponds to a real number. "Infinitesmals" are not real numbers so are not on a number line.
  13. Yes, the "natural basis" for [tex]R^2[/tex] is {(1, 0), (0, 1)}. Rotating (1, 0) through $\pi/3$ radians counter-clockwise gives [math](cos(\pi/3), sin(\pi/3))= (1/2, \sqrt{3}/2)[/math] and rotating (0, 1) through $\pi/3$ radians counter clockwise gives $(cos(4\pi/3), sin(4\pi/3)= (-sin(\pi/3), cos(\pi/3))= (-\sqrt{3}/2, 1/2)$. To represent that as a matrix, you need $\begin{pmatrix}a & b \\ c & d \end{pmatrix}$ so that $\begin{pmatrix}a & b \\ c & d \end{pmatrix}\begin{pmatrix}1 \\ 0 \end{pmatrix}= \begin{pmatrix}a \\ c \end{pmatrix}= \begin{pmatrix}1/2 \\ \sqrt{3}/2}\end{pmatrix}$ so a= 1/2 and $c= \sqrt{3}/2$. And, similarly $\begin{pmatrix}a & b \\ c & d \end{pmatrix}\begin{pmatrix}0 \\ 1 \end{pmatrix}= \begin{pmatrix}b \\ c \end{pmatrix}= \begin{pmatrix}\sqrt{3}/2, 1/2\end{pmatrix}$ so $b= -sqrt{3}/2$ and $d= 1/2$.
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